Tasaarv

Tasaarv is the Estonian term for an even number, a type of integer. Formally, an integer n is a tasaarv if there exists another integer k such that n = 2k. The set of tasaarvud includes numbers such as ..., -4, -2, 0, 2, 4, 6, 8, ... and constitutes the even integers.

In practical terms, a number is tasaarv if it is divisible by 2 without a remainder. In decimal notation, this is often observed by the last digit: numbers ending in 0, 2, 4, 6, or 8 are tasaarv, while those ending in 1, 3, 5, 7, or 9 are not. However, the core definition is arithmetic, independent of numeral systems.

Tasaarvud have several key properties. The sum or difference of two tasaarvud is a tasaarv. The product of a tasaarv and any integer is a tasaarv, and the product of two tasaarvud is also a tasaarv. The set of tasaarvud forms a subgroup of the integers under addition and a subring of the integers under the usual operations. Every integer is either a tasaarv or an odd number, and the parity of a number is determined by its remainder modulo 2: tasaarvud have remainder 0, odd numbers have remainder 1.

Tasaarvudd is widely used in basic arithmetic, number theory, and proofs that rely on parity arguments. They also underpin divisibility tests and modular arithmetic, where the concept of evenness plays a foundational role.